Pursuant to MCL 600.2918(3)(c), if you are accused of unlawful detainer it is a defense that "The owner believes in good faith that the tenant has abandoned the premises, and after diligent inquiry has reason to believe the tenant does not intend to return, and current rent is not paid."

I would start by making, and documenting, my diligent inquiry as to the tenant's intentions. If rent is unpaid, and diligent inquiry produces no response, I personally would repair the door and change the locks, post a note to the tenant (in a sealed envelope) indicating that the locks were changed in association with their abandonment and the need for repairs and they could contact me if they needed access, and send the tenant a notice of damages consistent with the state's security deposit laws.

If I were concerned that my actions might not be deemed diligent, or that the tenant might not have in fact abandoned the premises, with the thirty days being up I would file an eviction action, serve the tenant, and in all likelihood get a default judgment.